1. Field of the Invention
The present invention relates to a method for modeling the effects of interactions between wells on the watercut in effluents produced by an underground hydrocarbon reservoir under development, swept by a fluid under pressure, in order to optimize the reservoir production.
2. Description of the Prior Art
The production of water is a major problem in petroleum production. Operators can be confronted with situations where the watercut in the production of a well is very high whereas the in-place oil recovery ratio remains low, which clearly shows the ineffectiveness of a sweeping operation. They can be led to cease producing from the well concerned, with all the economic consequences entailed through lack of solutions allowing these water inflows to be controlled. It is within the scope of the production of stratified reservoirs swept by water, for example, that complex evolutions of this watercut can sometimes be observed.
It is well-known to treat locally a well where water inflows occur, by plugging the well zones producing water by injecting cement, polymers, gels, etc, and using packers in order to delimit the zones to be treated while the products are set. This technique is difficult to implement because the critical zones first have to be properly defined. Servicing operations are heavy and expensive, with no economic justification for wells that are often at the limit of profitability.
In order to contain great water inflows, it is also well-known to subject the reservoir to global treatments, for example by injecting polymers therein, the rate of success thereof remaining low and notably difficult to predict.
Reservoirs generally have very complex physics. Consider the case of a well crossing a certain number i of reservoir levels considered to be hydraulically independent in proportion to the environment of the well (i=2 in the case of FIG. 1). Under the effect of a draw-off with, for example, a flow rate Q imposed by a pump, the bottomhole pressure is expressed by the relations as follows: ##EQU1## where Pi is the pressure prevailing in bed i. The overall flow rate Q of the well is made up of the sum of the contributions Qi of all the beds i, each contribution depending on the productivity index IP.sub.i of the bed considered and on the pressure difference P.sub.1 -P.sub.wf applied. The watercut fw of the well results from an average of the watercuts fwi of each bed, weighted by the contribution thereof to the overall flow rate of the well.
The expression Qi=IPi (Pi-Pwf) shows that any variation Pi of the pressure Pi of a bed leads to a variation Qi of the flow rate Qi of the bed and, if the watercuts of the beds are different, to a variation of the watercut of the well according to the changes in the relative contributions of each bed to the overall production of the well. The variation Pi of the pressure of a bed can notably be due to a variation of the injection or production rates of the neighbouring wells. Besides, when the pressures in the various beds are substantially different, a variation of the production pressure P leads to a distribution variation of the flow rates (.alpha.i).
Furthermore, in cases where the pressures Pi of the various beds are substantially different, any change in the stress imposed on the well: flow rate Q of the pump or pressure P.sub.wf in the well, will lead to a variation of the watercut, an increase or a decrease according to the relative distributions of the saturations and of the pressures of each bed.